part -1:
1 Find the following values for a lump sum assuming annual compounding:
a. The future value of $500 invested at 8 percent for one year
b. The future value of $500 invested at 8 percent for five years
c. The present value of $500 to be received in one year when the opportunity cost rate is 8 percent
d. The present value of $500 to be received in five years when the opportunity cost rate is 8 percent
2 Repeat Problem 9.1 above, but assume the following compounding conditions:
a. Semiannual
b. Quarterly
3. Consider another ueven cash flow stream:
Year Cash flow
0 2,000
1 2,000
2 0
3 1,500
4 2,500
5 4,000
a. What is the present (year 0) value of cash flow stream if the opportunity cost rate is 10 percent?
b. What is the future (Year 5) value of the cash flow stream if the cash flows are invested in an account that pays 10 percent annually?
c. What cash flow today (year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000 at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.)
d. Time value analysis involves either discounting or compounding cash flows. Many health care financial management decisions such as bond refunding, capital investment, and lease versus buy involve discounting projected future cash flows. What factors must executives consider when choosing a discount rate to apply to forecasted cash flows?
4. Year Cash Flow
0 (1,000)
1 250
2 400
3 500
4 600
5 600
a. What is the return expected on this investment measured in dollar terms if the opportunity cost rate is 10 percent?
b. Provide an explanation, in economic terms, of your answer
c. What is the return on this investment measured in percentage terms?
d. Should this investment be made? Explain your answer.
Part -2
Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine:
State of Probability of
The Economy Occurrence Rate of Return
Very Poor 0.10 -10.%
Poor 0.20 0.0
Average 0.40 10.0
Good 0.20 20.0
Very Good 0.10 30.0
a. What is expected rate of return of the project?
b. What is the project's standard deviation of returns?
c. What is the project's coefficient of variation (CV) of returns?
d. What type of risk do the standard deviation and CV measure?
e. In what situation is this risk relevant?
2
Suppose that a person won the Florida lottery and was offered a choice of two prizes: (1) $500,000 or (2) a coin toss gamble in which he or she would get 1 million for heads and zero for tails.
a. What is expected dollar return on the gambler
b. Would the person choose the sure $500,000, or the gamble?
c. If she chooses the sure 500,000, is the person a risk averter or a risk seeker?
3
Company Beta
Quorum Health Group 0.90
Beverly Enterprises 1.20
Health South Corporation 1.45
United Healthcare 1.70
At the time these betas were developed, reasonable estimates for the risk-free ra te, RF and required rate of return on the market, R(Rm), were 6.5 percent and 13.5 percent, respectively.
a. What are the required rates of return on the four stocks?
b. Why do their required rates of return differ?
c. Suppose that a person is planning to invest in only one stock rather than a well-diversified stock portfolio. Are the required rates of return calcualated above applicable to the investment? Explain your answer?
4
Suppose that Apex Health Services has four different projects. These projects are listed below, along with the amount of capital invested and estimated corporate and market betas:
Amount Corporate Market
Project Invested Beta Beta
Walk in clinic 500,000 1.5 1.1
MRI Facility 2,000,000 1.2 1.5
Clinical Laboratory 1,500,000 0.9 0.8
X-ray laboratory 1,000,000 0.5 1.0
5,000,000
a. Why do the corporate and market beta differ for the same project?
b. What is the overall corporate beta of Apex Health Services?k Is the calculated beta consistent with corporate risk theory?
c. What is the overall market beta of Apex Health Services?
d. How does the riskiness of Apex's stock compare with the riskiness of an average stock?
e. Would stock investors require a rate of return on Apex that is greater than, less than, or the same as the return on an average risk stock?